Photonic devices having a waveguide provided on a substrate have been put in practical use. Recently, defect waveguide in two-dimensional photonic crystal (2D-PhC) have been attracting much attention, and much research and development efforts have been carried out. Specifically, a two-dimensional photonic crystal is formed by arranging regular pores in a thin film layer with a high refractive index (of Si or the like) to obtain a full photonic bandgap in the working frequency range in the planar direction (XZ-direction). When the 2D-PhC includes a linear defect, light entering the defective part is not able to exit to a photonic crystal portion and is confined therein. Therefore, the 2D-PhC can be used as a waveguide (see Patent Publication 1).
A waveguide employing a 2D-PhC has the characteristics described below.                Steep bending (by 60 or 90 degrees) is possible in the waveguide. Therefore, the individual photonic devices and the waveguide connecting the photonic devices can be made very compact.        A “group velocity anomaly” can be caused in electromagnetic waves propagated in the waveguide. This makes it possible to enhance the nonlinear effect to improve the characteristics and reduce the size of the device.        
The following are examples of optical devices employing a two-dimensional or three-dimensional photonic crystal waveguides or an ordinary waveguide without photonic crystal.                A directional coupler serving as optical multiplexer/demultiplexer (see Patent Publication 2)        An optical switch performing on-off operation in response to external electric current injection or light irradiation (see Patent Publication 3).        A symmetric Mach Zehnder all-optical switch (see Non-Patent Publication 1).        An optical delay line (See Non-Patent Publication 2)        A point-defect resonator (see Patent Publications 4 and 5)        
Propagated light of high-order photonic bands or high-order modes significantly varies its effective refractive index according to change in frequency. Therefore, confinement in the periodic direction of multilayer film core can be intentionally made weak to emit refracted light from the surface of the multilayer film which shows extremely large difference in refraction angle according to wavelength. This allows the optical device to function as a spectroscope. The present inventors have proposed a spectroscope utilizing such refracted light, some of which are released as spectroscope utilizing “high-order band propagation on the center of the Brillouin zone” (see Patent Publications 6 to 11, for example).
Patent Publication 1: Japanese Laid-Open Patent Publication No. 2001-281480
Patent Publication 2: Japanese Laid-Open Patent Publication No. 2001-174652
Patent Publication 3: Japanese Laid-Open Patent Publication No. 2002-303836
Patent Publication 4: Japanese Laid-Open Patent Publication No. 2001-272555
Patent Publication 5: Japanese Laid-Open Patent Publication No. 2003-161971
Patent Publication 6: Japanese Laid-Open Patent Publication No. 2002-236206
Patent Publication 7: Japanese Laid-Open Patent Publication No. 2002-169022
Patent Publication 8: Japanese Laid-Open Patent Publication No. 2002-182026
Patent Publication 9: Japanese Laid-Open Patent Publication No. 2002-267845
Patent Publication 10: Japanese Laid-Open Patent Publication No. 2003-240934
Patent Publication 11: Japanese Laid-Open Patent Publication No. 2003-287633
Non-Patent Publication 1: “Optronics”, April, 2002 edition, p. 132
Non-Patent Publication 2: “Photonic Crystal: Technology and Applications” CMC Publishing, 2002, p. 244
However, the conventional waveguides described above have problems as follows.
When the photonic crystal structure forming the waveguide is arranged in a square array, the angle of steep bending is limited to 90 degrees in most cases. Similarly, in the case of a triangular array, the angle is limited to 60 or 120 degrees. Accordingly, the waveguide, or various optical devices utilizing the waveguide cannot be arranged at a desired angle. This poses a design restriction.